Question

given $y = (2x + 3)^2$, choose the standard form of the given quadratic equation.
$\circ$ $0 = 25x^2$
$\circ$ $0 = 4x^2 + 9$
$\circ$ $0 = 4x^2 + 10x + 6$
$\circ$ $0 = 4x^2 + 12x + 9$
done

Explanation:

Step1: Expand the square

We use the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = 2x\) and \(b = 3\). So, \((2x + 3)^2=(2x)^2+2\times(2x)\times3 + 3^2\).

Step2: Calculate each term

\((2x)^2 = 4x^2\), \(2\times(2x)\times3 = 12x\), and \(3^2 = 9\). So, \((2x + 3)^2 = 4x^2 + 12x + 9\).

Step3: Rewrite the equation

Given \(y=(2x + 3)^2\), and we want to write it in standard form \(ax^2+bx + c = 0\) (where \(y = 0\) for the standard form of the quadratic equation). So, \(0 = 4x^2 + 12x + 9\) (by subtracting \(y\) from both sides, but since \(y=(2x + 3)^2\), we can directly set \(y = 0\) and expand).

Answer:

\(0 = 4x^2 + 12x + 9\) (the last option: \(0 = 4x^2 + 12x + 9\))